WASHINGTON (AP) -- Senate Republicans appeared Friday to push President Donald Trump's big bill back on track after a flurry of last-minute revisions, including deep cuts to food stamps, but there's still a long way to go ahead of expected weekend votes.

Trump himself gave Congress some breathing room as senators race to meet his Fourth of July deadline.

"It's not the end all," Trump declared during a press conference at the White House.

As the party in majority power, Republicans are grinding through a punch-list of still-unsettled issues as they try to push the package to passage over unified Democratic opposition. Republicans are relying on steep cuts to health care, food stamps and green energy investments to help pay for $3.8 trillion in tax breaks, their top priority. Any one of the roadblocks could doom the sprawling package.

The proposed Medicaid cuts, in particular, have raised stark concerns among some GOP senators worried that millions in their states will lose access to the health care program. At the same time, a tentative deal between the White House and House GOP lawmakers from New York and other high-tax districts over the size of a state and local tax deduction, called SALT, needs broader agreement.

House Speaker Mike Johnson, who sent his lawmakers home for the weekend with plans to be on call to return swiftly to Washington, said they are "very close" to finishing up.

"We would still like to meet that July 4th, self-imposed deadline," said Johnson, R-La.

Johnson and Senate Majority Leader John Thune have stayed close to the White House throughout the process of drafting the big package, which they stress is needed to avoid a massive tax hike at the end of the year when current tax rates expire. The GOP leadership is relying on Trump to pressure holdout lawmakers to push it to passage.

The speaker made the walk across the Capitol to join Senate Republicans for lunch, where they were also expected to meet with Treasury Secretary Scott Bessent over the emerging SALT deal.

"Perfect cannot be the enemy of good," Bessent said in remarks at the Faith and Freedom Conference in Washington. "Getting this passed is the single most important thing we can do this year."

The White House and House Republicans have narrowed on a plan to keep the SALT provision on the House-passed terms of a $40,000 cap on deductions -- but for five years, instead of 10.

The SALT deduction has been a key holdup as lawmakers from New York and other high-tax states negotiate. They want to quadruple what's now a $10,000 cap. Senate Republicans argued that it's too generous, costing hundreds of billions of dollars for the benefit of a few lawmakers' home regions.

With their narrow majorities in the House and Senate, they need almost every lawmaker on board with the package to ensure passage. One GOP holdout, Rep. Nick LaLota of New York, says he can't support the compromise.

But other provisions were being shored up after a series of setbacks when the Senate parliamentarian advised they would not pass the chamber's strict "Byrd Rule" that largely bars policy matters from inclusion in budget bills, unless they can pass the 60-vote threshold that GOP leaders want to avoid.

The Republican proposal to shift the costs of the Supplemental Nutrition Assistance Program, known as SNAP, has been accepted by the Senate parliamentarian.

Sen. John Boozman of Arkansas, the chairman of the Senate Agriculture Committee, said provisions to make certain immigrants ineligible for food aid were also accepted.

"This paves the way for important reforms that improve efficiency and management of SNAP," he said.

But the panel's top Democrat, Sen. Amy Klobuchar of Minnesota, said her party will "keep fighting these proposals that raise grocery costs and take food away from millions of people, including seniors, children, and veterans."

The nonpartisan Congressional Budget Office has said some 10.9 million more people will go without health care and at least 3 million fewer would qualify for food aid under the House-passed bill. CBO has not yet publicly assessed the Senate draft, which has proposed steeper reductions.

The top income earners would see about a $12,000 tax cut under the House-passed bill, while the poorest Americans would see a $1,600 tax hike, the CBO said.

The parliamentarian also accepted a revised proposal from the Senate Banking Committee to cut, rather than gut, the funding structure for the Consumer Financial Protection Bureau. The entity was set up in the aftermath of the 2008 financial crisis, but Trump has downsized the bureau and its staff.

Still, a range of GOP provisions have been found to be out of compliance with Senate rules -- including shielding gun silencers from taxes and creating a national school voucher program.

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Associated Press writers Kevin Freking, Joey Cappelletti, Fatima Hussein, Seung Min Kim and Chris Megerian contributed to this report.